Dynamic behavior of a discrete modified Ricker & Beverton–Holt model

In this paper, a discrete modified Ricker & Beverton–Holt model with two parameters is investigated. The boundedness, the persistence, and the global asymptotic stability are considered. At the same time, in the unstable domain the chaotic behavior will be shown for some particular parameters. Usually, chaos can cause the population to run a higher risk of extinction and make the population become out of control due to the unpredictability. To control the unpredictability, the immigration parameter will be introduced. When the immigration constant is larger than a positive number, chaos will be controlled and the positive equilibrium is stable. Furthermore, the obtained results show that the reproduction rate of adults plays an important role in the process of the population.